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P2.T7.302. Liquidity risk: liquidity-adjusted value at risk (VaR) models

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302.1. Malz gives us the following adjustment which estimates a liquidity-adjusted VaR based on the number of trading days (T) required to liquidate a position:



Portfolio Manager Sally holds an equity portfolio with a value of $10.0 million and volatility of 18.0% per annum. She estimates it would require ten (10) trading days to liquidate the portfolio. If there are 250 trading days in a year, which is nearest to the 99.0% confident liquidity-adjusted VaR?

a. $264,836
b. $433,725
c. $519,646
d. $623,080

302.2. You are analyzing an equity position of 100,000 shares in an illiquid, non-public stock which has a current price of USD 44.00 per share. The estimated daily return volatility is 80 basis points (0.80%). The bid-ask spread is USD 0.11. If you assume the daily expected return is zero and the bid-ask spread is constant, which is nearest to the one-day 95% liquidity-adjusted value at risk (VaR)? (This question inspired by FRM Handbook Question 26.6)

a. $38,500
b. $49,250
c. $57,780
d. $63,400

302.3. You are manager of a distressed fund with a position in the Wheelbarrow Company. You hold 100,000 shares in this illiquid stock which has a current price of $96.00 per share. The volatility of the stock is 42.0% per annum. The spread is not constant: it has a mean of 2.0% with volatility of 1.0%. You assume the daily expected return of the stock is zero such that absolute and relative VaR give the same result. Because the spread is not constant, you are going to employ what Jorion calls the worst-case liquidity-adjusted VaR and what Dowd calls the exogenous random spread approach. If you assume 250 trading days per year, which is nearest to the one-day 99.0% LVaR under an exogenous random spread approach? (This question inspired by FRM Handbook question 26.5)

a. $594,165
b. $689,230
c. $733,334
d. $800,900

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